1. Field of the Invention
This invention relates generally to systems and methods for recording and processing time series data, i.e., numeric data that are recorded in time sequence, and particularly to a system and method for predicting an extreme change in a time series given past given past values of the series using symbol extraction.
2. Discussion of the Prior Art
One problem that often arises when recording and processing time series data is that the numeric data are too noisy. Noise can be due to measurement error of the time series, or due to process noise which arises in situations where the data that are measured are subject to shocks due to the data generation process. For example, in a stock market scenario, where a future stock value (of a time series) is to be predicted given past values of the series, each stock price at a given time is due to the impact of every trader on the market. Thus, it is said that the measurements are due to process noise. In these events, it is necessary to invoke xe2x80x9cnoise reduction strategies,xe2x80x9d i.e., methods to reduce the noise present in the observations.
Signal processing technology is replete with numerous noise reduction techniques. The following references: Scharf, et. al. entitled L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis (New York: Addison-Wesley Publishing Co., 1990); L. L. Scharf, xe2x80x9cThe SVD and Reduced Rank Signal Processing,xe2x80x9d Chapter 1 in The SVD and its Applications, R. Vaccaro, ed. (Elsevier, 1991); and, xe2x80x9cDigital Signal Processing,xe2x80x9d by Richard A. Roberts, Clifford T. Mullis (Contributor). Hardcover (February 1987) outline some of the well-known noise reduction strategies. One particular signal processing noise reduction technique is known as singular value decomposition as described in the reference to C. R. Rao entitled xe2x80x9cLinear Statistical Analysis and its Applicationsxe2x80x9d (1963).
Another method for processing time series signals, in particular, utilizes moving average techniques to reduce noise. Moving averages are computed by taking subsets of sequences of numbers, computing the average of those numbers, recording the result, and then shifting the subset by one unit in time. Other noise reduction techniques include the application of a digital filter. Essentially, most of the noise reduction techniques rely on moving averages of the data, which do not generate symbol sequences.
It would be highly desirable to provide an improved method and mechanism for forcasting future time series values, and particularly, extreme events, based on past time series data values.
It would additionally be highly desirable to provide an improved method for processing time series signals in which a time series is converted to a symbol sequence comprising sets of finite symbols which may be used as a basis for forcasting future time series values.
It is an object of the present invention to provide a method for extracting symbols from a numeric time series of data which symbols provide the basis for forecasting values from future time series.
According to the invention, there is provided a method for extracting symbols from a numeric time series comprising the steps of: receiving a finite time series of data elements for a particular application, the data elements characterized as having one or more sharp changes in values; for each sharp change in the finite time series, extracting a window of elements from the time series that precedes each sharp change; building a matrix from the time series window extracts; performing singular value decomposition on the built matrix to obtain characteristic matrices; and, obtaining vectors of symbols from resulting characteristic vectors determined from the singular value decomposition step, wherein the resulting symbols are used by forecasting algorithm to predict a future sharp change in subsequent finite time series received for the application.
Advantageously, the sets of finite symbols obtained may be used as the basis for applications requiring the prediction of an extreme change in a received time series.